David Luiz is an extremely accomplished footballer, but one without a natural home on the pitch. His ability to do good with the ball at his feet is not in question, but unfortunately neither is his tendency to do harm without it.
Chelsea have shifted the Brazilian into midfield lately, and while there are obvious benefits to having him in that role, he very much looks like someone playing the position from a handbook – it’s not natural. Additionally, the lack of responsbility he showed at centre-back has really just been shifted into midfield now – he’s the same liability, just in a different way. Luiz is not the best tackler, he doesn’t have the discipline to track runners from midfield who go beyond him, and that’s obviously a problem against good sides.
How about using him as a full-back? It’s a hypothetical situation obviously, but theoretically it should work. Luiz would have the license to go forward and join the attack, but without having such a pivotal defensive role. Playing at right-back obviously has defensive duties that come with it, but not to the same extent that a central role does. One player to mark, maybe with an overlapping second; a simplified assignment for a player who struggles in his own half.
Offensive there would be no problem: Luiz has the pace to play out-wide and the ball-skills and vision to be a useful attacking outlet. It might be a disaster, but it also might be the position on the pitch which best fits his physical and mental attributes.